The period of the pendulum when the length is 3 ft is approximately 2.08 seconds.
What is the period?
We are given that the period P varies directly as the square root of the length L of the pendulum. We can write this as:
P ∝ √L
Using a proportionality constant k, we can write this as an equation:
P = k√L
To find the value of k, we can use the information given in the problem: when L = 2 ft, P = 1.8 s. Substituting these values into the equation, we get:
1.8 = k√2
To solve for k, we can isolate it by dividing both sides by √2:
k = 1.8 / √2
Now we can use this value of k to find the period when the length is 3 ft. Substituting L = 3 ft and the value of k we just found into the equation, we get:
P = k√L
P = (1.8 / √2) √3
P ≈ 2.08 seconds
Therefore, the period of the pendulum when the length is 3 ft is approximately 2.08 seconds.
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Are √2 and √√32 like radicals? Can the sum be simplified?
Answer:
simplifies to 5[tex]\sqrt{2}[/tex]
Step-by-step explanation:
using the rule of radicals
[tex]\sqrt{ab}[/tex] = [tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex]
then
[tex]\sqrt{32}[/tex] = [tex]\sqrt{16(2)}[/tex] = [tex]\sqrt{16}[/tex] × [tex]\sqrt{2[/tex] = 4[tex]\sqrt{2}[/tex]
then
[tex]\sqrt{2}[/tex] + [tex]\sqrt{32}[/tex]
= [tex]\sqrt{2}[/tex] + 4[tex]\sqrt{2}[/tex] ( the 2 terms have like radicals so add coefficients )
= 5[tex]\sqrt{2}[/tex]
The distance from the Earth to the sun is 93 million miles or 93,000,000 miles. How would this number be written in scientific notation?
Answer: To write 93,000,000 in scientific notation, we need to move the decimal point to the left so that there is one non-zero digit to the left of the decimal point.
Counting the number of places we move the decimal point, we get:
93,000,000 = 9.3 x 10^7
Therefore, 93 million miles can be written in scientific notation as 9.3 x 10^7 miles.
Step-by-step explanation:
The number of users on a website is 6300 and is growing exponentially at a rate of
73% per year. Write a function to represent the number of users on the website after t
years, where the daily rate of change can be found from a constant in the function.
Round all coefficients in the function to four decimal places. Also, determine the
percentage rate of change per day, to the nearest hundredth of a percent.
The percentage rate of change per day is approximately 0.1932%.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
To represent the number of users on the website after t years, we can use the exponential growth formula:
[tex]N_t = N_0 \times e^{rt}[/tex]
where [tex]N_0[/tex] is the initial number of users, r is the growth rate, and t is the time in years.
Given that [tex]N_0[/tex] = 6300 and the growth rate is 73%, or 0.73, per year,
The function is:
[tex]N_t = 6300 \times e^{0.73t}[/tex]
To find the percentage rate of change per day, we can use the formula:
[tex]r = (e^{0.73/365} - 1) \times 100%[/tex]
where 0.73/365 is the daily growth rate.
Solving for r, we get:
[tex]r = (e^{0.73/365} - 1)[/tex] x 100%
r ≈ 0.1932%
Therefore,
The percentage rate of change per day is approximately 0.1932%.
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you move left 1 unit and move up one unit you end up at 10,0 what did you start with
Answer:
the coordinate is (11,1)
How does f(x)=x change over the interval from x=2 to x=9?
Answer:
The function f(x) = x represents a straight line with a slope of 1, passing through the origin (0,0).
If we consider the interval from x = 2 to x = 9, we can see that the line starts at f(2) = 2 and ends at f(9) = 9.
Therefore, over the interval from x=2 to x=9, the function f(x) = x increases in a straight line fashion from 2 to 9.
In other words, the slope of the line is positive, and the function is monotonically increasing on this interval.
What is the value of -1/6+2/3(9-3/4)-1/2
A. 62/12
B. 58/12
C. 55/12
D. 3/12
Answer:
The given expression is,
-1/6+2/3(9-3/4)-1/2
According to BODMAS rule, we first do the operation of bracket ( as B comes first in the BODMAS).
∴ 9-3/4= (36-3)/4=33/4
Putting 33/4 in place of (9-3/4), the expression becomes
-1/6+2/3×33/4-1/2
Now, the priority of M in BODMAS is more than A and S, so we do the operation of multiplication.
∴2/3×33/4=11/2 ( as 33÷3=11 and 4÷2=2)
Replacing 2/3×33/4 by 11/2, the expression becomes,
-1/6+11/2-1/2
= -1/6+(11-1)/2
= -1/6+5
= (-1+30)/6
=29/6
Hence the value of the given expression is 29/6.
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Can anyone help me rq?
Answer:
⅙
Step-by-step explanation:
I just know the answer cuz I am better
Tom and John are engaged in buying and selling certain products A and B. Tom BUYS 5 of product A but
SELLS twice as much of product B. John on the other hand SELLS three times what Tom BOUGHT of
product A and BUYS 13 of product B. At the end of the business day, John banks Ksh 110,000/- while
Tom banks Ksh 230,000.
Under the assumption that the sale prices for product A and B are the same for the two men, and the
costs prices for the products A and B are also the same for the two men, obtain the following:
a) The price for product A and the price for product B (5 marks)
b) If there was a mark up of 25% on the cost price and a discount of 15% on the sale price, how
much would each of the partners have banked at the end of the business day? (10 marks)
Answer:Let's assume that the cost price for both products A and B is "C", and the selling price for both products A and B is "S". We can use this information to set up two equations, one for Tom and one for John, that relate the costs and profits for the two products:
Tom: 5C - 2(5S) = P1
John: 3(5C) - 13C = P2
where P1 and P2 are the profits made by Tom and John, respectively.
We know that at the end of the business day, John banks Ksh 110,000/- while Tom banks Ksh
230,000. So we can write:
P1 = 230,000 - 5C
P2 = 110,000 - 18C
Substituting these values into the equations for Tom and John, we get:
5C - 2(5S) = 230.000 - 5C
Simplifying these equations, we get:
10C - 10S = 230,000
2C = 110,000
Solving for C, we get:
C = 55,000
Substituting this value back into the first equation, we can solve for S:
10(55,000) - 10S = 230,000
Simplifying this equation, we get:
S = 32,000
Therefore, the price for product A is Ksh 55,000 and the price for product B is Ksh 32,000.
Step-by-step explanation:
Pleaee Help apap. THANKS
Answer:
36 sq. inches assuming the shapes are same as well as sides
In a board game, the cards you draw tell how many spaces to move. Which expression gives the total number of spaces traveled during the 4 turns?
The expression-4 gives the total number of spaces traveled during the 4 turns can be found using integers or its absolute values.
What are integers?
Integers are the collection of negative, positive numbers including zero. The positive integers lie on the right side of the zero on the number line and the negative lie on the left side of zero on number line. The positive numbers are larger than the negative numbers. Also zero is greater than all negative numbers.The absolute value/modulus of any integer is its magnitude without sign. It is the distance of any given integer from zero.
Here the spaces travelled in each turn is given as +7, +2, +5 and -8.
The total sum of the spaces=(+7) + (+2) + (+5) + (-8)
= 7+2+5-8
=6
The expression in option 1: |7 + -2 + 5 + - 8| which is not equal to 6
The expression in option 2: 7 - 2 + 5 - 8 which is not equal to 6
The expression in option 3: |(+7) + (-2) + (+5) + (- 8)| which is not equal to 6
The expression in option 4: |7 | + |-2| + |5| + |- 8| which is equal to 6
∴The correct expression is option-4
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Sumi owns a plant store she wants to put 438 plants in 7 equal rows How many plants will be left over after putting them in do
There will be 4 plants left over after putting them in 7 equal rows.
Calculating the number of left over plantsTo find out how many plants will be left over after putting them in 7 equal rows, we need to divide the total number of plants (438) by the number of rows (7) and then find the remainder.
We can use integer division to find out how many plants will be in each row:
438 ÷ 7 = 62
So each row will have 62 plants.
To find out how many plants will be left over, we can subtract the total number of plants from the product of the number of rows and the number of plants in each row:
438 - (7 x 62) = 438 - 434 = 4
Therefore, the number of plants remaining is 4 plants
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Find the area of the parallelogram 9m 4m A=b×h =[].9 =[]m2
Answer:
Step-by-step explanation:
<
8
Which equation could be used to solve for mº?
49⁰
32°
A 49° +32° + m² = 180°
B 49° +32° + m² = 90°
c) 49° +32° = mᵒ
(D) 49 = 32° +m
mº
In the given equation the value of mº is 17°. Answer: (D) 49 = 32° + mº.
What do you mean by the term Triangle and kinds of triangle ?A triangle is a geometrical figure with three straight sides and three angles. It is the simplest polygon and the building block for more complex shapes.
There are several kinds of triangles:
Equilateral triangle: This is a triangle with three equal sides and three equal angles of 60 degrees each.
Isosceles triangle: This is a triangle with two equal sides and two equal angles.
Scalene triangle: This is a triangle with no equal sides or angles.
Right-angled triangle: This is a triangle with one angle of 90 degrees, which is also known as the right angle. The side opposite to the right angle is the longest side, called the hypotenuse, while the other two sides are called legs.
Acute triangle: This is a triangle in which all three angles are acute angles, meaning they are less than 90 degrees.
Obtuse triangle: This is a triangle in which one angle is an obtuse angle, meaning it is greater than 90 degrees. The other two angles are acute angles.
The equation that can be used to solve for mº depends on the given information or conditions. If the problem provides the measures of two angles and their sum, then we can use the equation:
A + B + m = 180°
where A and B are the measures of the given angles, and m is the measure of the unknown angle in degrees.
However, if the problem only gives the measures of two angles and their sum is not required, we can use the equation:
A + B = m
where A and B are the measures of the given angles, and m is the measure of the unknown angle in degrees.
Based on the given information in the question, we are only provided with the measures of two angles, 49° and 32°, and there is no indication that their sum is required. Therefore, the correct equation to solve for mº is:
49° = 32° + mº
We can simplify this equation to solve for mº:
49° - 32° = mº
mº = 17°
Therefore, the value of mº is 17°. Answer: (D) 49 = 32° + mº.
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Use the triangular prisons below to answer questions 6-9. Be sure to show all steps and work.
The prism A have lateral surface area = 685 and total surface area = 1021, while the prism B have lateral surface area = 328 and total surface area = 448.
How to calculate for the lateral and total surface area of the triangular prismsThe triangular prisms A and B have two same size triangle faces and two different size rectangle face with a rectangle bottom face.
For 6 and 7;
area of one triangle face = 1/2 × 21 × 9
area of one triangle face = 94.5
area of the two triangle faces = 2(94.5) = 189
area of one smaller rectangle face = 16 × 14 = 224
area of one bigger rectangle face = 17 × 16 = 272
Area of lateral surface area = 188 + 224 + 272 = 685
Area of bottom rectangle face = 21 × 16 = 336
Total surface area of prism A = 685 + 336 = 1021
For 8 and 9;
area of one triangle face = 1/2 × 24 ×
area of one triangle face = 84
area of the two triangle faces = 2(84) = 168
area of one smaller rectangle face = 7 × 5 = 35
area of one bigger rectangle face = 25 × 5 = 125
Area of lateral surface area = 168 + 35 + 125 = 328
Area of bottom rectangle face = 24 × 5 = 120
Total surface area of prism A = 328 + 120 = 448
Therefore, the prism A have lateral surface area = 685 and total surface area = 1021, while the prism B have lateral surface area = 328 and total surface area = 448.
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Fine the surface area of the prism.
The surface area is ? square feet.
By answering the presented question, we may conclude that As a result, surface area the prism's surface area is 640 square feet.
what is surface area ?The surface area of an object indicates the overall space occupied by its surface. The surface area of a three-dimensional form is the entire amount of space that surrounds it. The surface area of a three-dimensional form refers to its full surface area. By summing the areas of each face, the surface area of a cuboid with six rectangular faces may be computed. As an alternative, you may use the following formula to name the box's dimensions: 2lh + 2lw + 2hw = surface (SA). Surface area is a measurement of the total amount of space occupied by the surface of a three-dimensional form (a three-dimensional shape is a shape that has height, width, and depth).
To get the surface area of the prism, sum the areas of all six faces.
The top and bottom rectangular faces have the same size and area:
10 feet x 8 feet = 80 square feet
The dimensions of the other four faces are the same:
12 feet tall x 10 feet wide = 120 square feet
As a result, the total surface area is:
2 (80 square feet) + 4 (120 square feet) = 160 square feet + 480 square feet = 640 square feet
As a result, the prism's surface area is 640 square feet.
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Circle S is shown where points V, P, and T lie on the circle and tangent lines VK and T'K intersect at point K.
p
S
K
If mVPT = 234° what is the measure of angle LVKT?
In the tangent line , Value of [tex]m\angle{VKT}[/tex] is A)54°.
What is tangent line in the circle?A circle's tangent is a single-pοinted line that intersects the circle. The "pοint οf tangency" is the lοcatiοn where the circle and the tangent crοss. The radius οf the circle, with which it crοsses, is perpendicular tο the tangent. All curved shapes can be thοught οf as tangent. As a tangent is a line, it has an equatiοn as well.
The line that οnly tοuches the circumference οf a circle οnce is said tο be tangent tο it. Fοr each circled pοint, there can οnly be οne tangent. The tangent's pοint οf tangency is where it jοins the circle.
Here the given circle arc length mVPT = 234°. Then
arc length οf mVT = 360°-234° = 126°
Nοw using tangent line fοrmula in circle then,
=> [tex]m\angle{VKT}=\frac{mVPT-mVT}{2}[/tex]
=> [tex]m\angle{VKT} =\frac{234\textdegree-126\textdegree}{2}[/tex]
=> [tex]m\angle{VKT} =\frac{108\textdegree}{2} =54\textdegree[/tex].
Hence the correct option is A)54°.
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If f (x) = 3x, g (x) = x + 4, and h (x) = x^2 - 1, find [fo(hog)] (1)
Answer:
Step-by-step explanation:
To find [fo(hog)] (1), we need to first evaluate the composition hog at x = 1, and then plug the result into f.
Let's start by evaluating hog at x = 1:
hog(x) = h(g(x)) = h(x + 4) = (x + 4)^2 - 1
So, hog(1) = (1 + 4)^2 - 1 = 24
Now we can evaluate f at hog(1):
f(hog(1)) = f(24) = 3(24) = 72
Therefore, [fo(hog)] (1) = 72.
3. Radioactive tracers are used when imaging the brain. A certain tracer has a
half-life of 5.0 hours.
a. Write the equation of the half-life that models the decay of 20mg.
b. During which hour will the initial amount decay to 5mg?
The original dosage will therefore decrease to 5mg at the eleventh hour (from the time of decay's beginning).
how to solve an equation ?A logical statement that two forms are equal is known as an equation. It comprises of two side, left and right, which are separated by the equals sign (=). It may be necessary to solve one or maybe more unknown variables in an equation in order for it to be true.
As an illustration, the expression 3x + 5 = 14 has one unknown quantity, x. In order to solve for x, we must rewrite the equation using operations that preserve equality, such as deducting 5 both from sides of the equation:
given
We may change A = 5 into the equation above and solve for t to get the time at which there are 5mg left: 5 = 20(1/2)(t/5)
20 divided by both sides:
Using base 2, take the logarithm of both sides:
log2(1/4) = t/5 -2 = t/5
t = -10 after multiplying both sides by 5.
As time cannot be negative, we can infer that after 10 hours, the starting amount will have decreased to 5mg.
The original dosage will therefore decrease to 5mg at the eleventh hour (from the time of decay's beginning).
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The area of a square is 49 mm.
What is the length of each side?
Answer:
Area = 49 mm
Answer:
Step-by-step explanation:
Can someone help me with these two questions please?
Answer:
Step-by-step explanation:
Find each length below.
a) The length of the secant segment [tex]HC = 31.5[/tex].
b) The length of the secant segment [tex]XY = 4.8[/tex]
What is the secant segment?In geometry, a secant is a line that intersects a circle at two distinct points. A secant segment is part of a secant that lies between its two points of intersection with the circle.
In geometry, a segment is part of a line that is bounded by two distinct endpoints. A segment can be straight or curved. Straight segments are also called line segments, and curved segments are also called arcs.
According to the given information
a) In the figure, HG is a tangent and HD is a secant to the circle, and HC is the length of the secant segment.
We know that the product of the lengths of the two segments of a secant from an exterior point to a circle is equal to the product of the lengths of the entire secant and its external segment. That is,
[tex]HD*HE =HG^{2}[/tex]
where [tex]HE[/tex] is the length of the external segment of the secant.
Substituting the given values, we get:
[tex]31.5*HE =21^{2}[/tex]
[tex]HE = 21^{2} /31.5 = 14[/tex]
Now, we can use the same property to find [tex]HC[/tex]. That is,
[tex]HC *HE =HG^{2}[/tex]
Substituting the values we have found, we get:
[tex]HC*14 = 21^{2} \\HC = 21^{2} /14 = 31.5[/tex]
Therefore, the length of the secant segment [tex]HC = 31.5[/tex].
b) [tex]VX*VZ= VY*VW[/tex]
Substituting the given values, we get:
[tex]14.4*12= VY *36\\VY = (14.4*12)/36 = 4.8[/tex]
Therefore, the length of [tex]VY, XY = 4.8[/tex]
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Solve the right triangle. Round your answers to the nearest tenth.
m∠A = _____ degrees
m∠B = _____ degrees
AB = ____ units
(40 points)
Answer:
m∠A = 50°
m∠B = 40°
AB = 15.5 units
Step-by-step explanation:
This is a right trangle, so we can use the Pythagorean Theorem to calculate AB.
AC² + BC² = AB²
AB² = 11.9² + 10²
AB² = 141.61 + 100
AB = √241.61
AB ≈ 15.5 units
Since this is a right triangle, we only need the angle measurement of either m∠A or m∠B to calculate the angle measurement of the other.
I will use sine function to calculate the angle measurements of A and B. Try to use a more precise value for AB than the rounded answer so our angle measurement will be closer to the actual angle.
sin(m∠B) = 10/15.54381
m∠B = sin⁻¹(10/15.54381)
m∠B = 40.04°
Round to nearest tenth, so m∠B = 40°
m∠A + m∠B + 90° = 180°
m∠A + 130° = 180°
m∠A = 50°
The students at Woodward Elementary voted for a school mascot. The falcon won with 5/8 of the votes and the eagle came second with 1/3 of the remaining votes. If 536 students voted for a mascot, how many students voted for the eagle
Approximately 75 students voted for the eagle.
Define fractionA fraction is a numerical quantity that represents a part of a whole or a quotient of two numbers. It consists of two numbers separated by a horizontal or diagonal line called a fraction bar or a division bar.
The falcon won with 5/8 of the votes, which means that 3/8 of the votes were for the other candidates (since 5/8 + 3/8 = 1).
Let's represent the total number of votes as "x".
Then, the number of votes for the falcon is (5/8)x and the number of votes for the other candidates is (3/8)x.
Out of these other candidates, the eagle received 1/3 of the votes. So, the number of votes for the eagle is:
(1/3)(3/8)x = (1/8)x
We know that the total number of votes is 536, so we can set up the equation:
(5/8)x + (3/8)x + (1/8)x = 536
Simplifying the equation, we get:
(9/8)x = 536
Multiplying both sides by 8/9, we get:
x = 596
Therefore, the number of votes for the eagle is:
(1/8)x = (1/8)(596) = 74.5
Therefore, approximately 75 students voted for the eagle.
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Margot gave 12% of x number of dollars that she earned over the summer to an animal rescue shelter.
12% of x is about $60.00. Select all the statements that are true.
Thus, the total earning of Margot during summer is found to be $500.
Explain about the percentage of number:Although the usage of percent and percentage differs slightly, they both signify the same thing. It is customary to use percent or the symbol (%) along with a numerical value.
Although the percentage word was not very ancient, the technique was often used. The Ancient Romans used to calculate fractions as multiples of 1/100 in the absence of the decimal system.
Given :
Let the total earning of Margot be 'x'.Donated amount to animal rescue shelter. = $60Percentage - 12%So,
12% of x = 60.00
x = 60.0 * 100 / 12
x = $500
Total earning amount = $500
Thus, the total earning of Margot during summer is found to be $500.
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Correct question:
Margot gave 12% of x number of dollars that she earned over the summer to an animal rescue shelter.
12% of x is about $60.00. Find the total earning of Margot during summer.
solve for all solutions of cos(2x)cos(x)-sin(2x)sin(x)=1
The solutions to the original equation are x = 2nπ, where n is an integer.
What is trigonometric identity?A trigonometric identity is an equation that is true for all values of the variables within the domain of the functions involved.
According to question:We can use the trigonometric identity cos(2x) = cos²(x) - sin²(x) to simplify the left-hand side of the equation:
cos(2x)cos(x) - sin(2x)sin(x) = (cos²(x) - sin²(x))cos(x) - 2sin(x)cos(x)sin(x)
Simplifying further using the identity sin(2x) = 2sin(x)cos(x), we get:
(cos²(x) - 3sin²(x)cos(x)) + sin(2x) = 1
Substituting sin(2x) = 2sin(x)cos(x), we get:
cos³(x) - 3sin²(x)cos(x) + 2sin(x)cos(x) - 1 = 0
We can factor this expression as follows:
(cos²(x) - 1)(cos(x) - 2sin(x) + 1) = 0
The first factor has solutions cos(x) = ±1, which means x is an integer multiple of π/2. However, these solutions do not satisfy the original equation, since the left-hand side is always equal to zero.
The second factor gives us the equation cos(x) - 2sin(x) + 1 = 0. We can rewrite this as:
cos(x) + 1 = 2sin(x)
Using the identity sin²(x) + cos²(x) = 1, we can square both sides of this equation to get:
1 + 2cos(x) + cos²(x) = 4sin²(x)
Substituting sin²(x) = 1 - cos²(x), we get:
5cos²(x) - 4cos(x) - 3 = 0
This quadratic equation can be factored as:
(5cos(x) + 3)(cos(x) - 1) = 0
The first factor gives us the solution cos(x) = -3/5, but this is not a valid solution since the cosine function only takes values between -1 and 1.
The second factor gives us the solution cos(x) = 1, which means x is an integer multiple of 2π.
Therefore, the solutions to the original equation are:
x = 2nπ, where n is an integer.
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Simplify (4x − 6) − (5x + 1).
Answer:
[tex] - x - 7[/tex]
Step-by-step explanation:
[tex](4x - 6) - (5x + 1)[/tex]
A minus before the parentheses changes the signs in the parentheses to the opposite:
[tex] 4x - 6 - 5x - 1[/tex]
Subtract the number with x's seperately from the plain numbers:
[tex]4x - 5x - 1 - 6[/tex]
[tex] - x - 7[/tex]
Geometry. Find the value of the variable.
Using intersecting secant theorem, the value of x is approximately 6
How to find the value of the variableThe value of the variable is solved using intersection secant theorem
The theorem gives the formula applied as follows
(6 + 6) * 6 = (5 + x) * x
Starting with the left side of the equation:
(6 + 6) * 6 = 12 * 6 = 72
Now, let's simplify the right side of the equation:
(5 + x) * x = 5x + x^2
Substituting these simplified expressions back into the original equation, we get:
72 = 5x + x^2
This is now a quadratic equation, which we can solve by rearranging and factoring:
x^2 + 5x - 72 = 0
Using calculator the solution is x = 6.35 or -11.35
Taking the positive value we have that x = 6.35
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HELP ASAP PLEASE THIS IS PAST DUE SO YAH HELP AND BRAINLIEST
What is the area of a right triangle with a height of seven and three fourths yards and a base of 20 yards?
140 yds2
155 yds2
thirty eight and three fourths yds2
seventy seven and one half y
Answer: If the height of seven and three fourths yards and a base of 20 yards, then the area of the right triangle is 77.5 square yards.
To calculate the area of a right triangle, we can use the formula:
Area = (base * height) / 2
where the base is one of the sides of the triangle, and the height is the perpendicular distance from that side to the opposite vertex.
In this case, the height of the right triangle is 7 and 3/4 yards, and the base is 20 yards. Plugging these values into the formula, we get:
Area = (20 * 7.75) / 2 = 155 / 2 = 77.5 square yards
In summary, to calculate the area of a right triangle, we can use the formula that relates the base and height to the area. In this case, we needed to use the given values of the height and base of the right triangle to compute the area in square yards.
The resulting area represents the amount of surface inside the triangle and is useful in many applications, such as geometry, physics, and engineering.
Step-by-step explanation:
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Colby went to the bookstore traveling 12 mph and returned home traveling 10 mph. If the total trip took 11 hours, how long did Colby travel at each speed?
____ hours at 12 mph
____ hours at 10 mph
Thus, the time taken by Colby to travel at each speed is-
5 hours at 12 mph and 6 hours at 10 mph.
Define about the relation of speed and time:In the study of physics, the three key variables are speed, distance, and time. How quickly or slowly an object moves through one point to another is determined by the concept of speed. The distance travelled in a unit of time is referred to as speed. Distance is exactly proportional to velocity and speed, while time is constant.
The formula for speed:
speed = distance/time
Then ,
time = distance / speed
Let speed S1 = 12 mph , for this time taken t1.
Let the speed S2 = 10 mph , for this time taken t2.
Since, in each distance is same say 'd'.
Total time t = 11 hours.
t = t1 + t2
t = d/s1 + d/s2
11 = d(1/12 + 1/10)
11 = d(12+10) / (12*10)
d = 11*120 / 22
d = 60 miles.
t1 = 60/12 = 5 hours
t2 = 60/10 = 6 hours.
Thus, the time taken by Colby to travel at each speed is-
5 hours at 12 mph
6 hours at 10 mph
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Evaluate the function using the Maclaurin series
we use the first four terms, we get: equation.
[tex]f(x) =x^2 + x^3 + x^4/2! + x^5/3![/tex]
And so on.
What is Maclaurin series?A Maclaurin series, named after the Scottish mathematician Colin Maclaurin, is a special type of power series expansion of a function that is centered at zero. In other words, it is a way to represent a function as an infinite sum of terms that involve the function's derivatives evaluated at zero.
The general form of a Maclaurin series for a function f(x) is given by:
[tex]f(x) = f(0) + f'(0)x + (f''(0)/2!)x^2 + (f'''(0)/3!)x^3 + ...[/tex]
To evaluate the function f(x) = x^2 * [tex]e^x[/tex] using Maclaurin series, we can first find the Maclaurin series for [tex]e^x[/tex] and then multiply it with x^2 to obtain the Maclaurin series for f(x).
The Maclaurin series for [tex]e^x[/tex]is given by:
[tex]e^x = 1 + x + x^2/2! + x^3/3! + x^4/4! + ...[/tex]
Multiplying both sides by x^2, we get:
[tex]x^2 * e^x = x^2 + x^3 + x^4/2! + x^5/3! + x^6/4! + ...[/tex]
Therefore, the Maclaurin series for f(x) is:
[tex]f(x) = x^2 * e^x = x^2 + x^3 + x^4/2! + x^5/3! + x^6/4! + ...[/tex]
To approximate the value of f(x) using the Maclaurin series, we can truncate the series after a certain number of terms. The more terms we include, the more accurate the approximation will be. For example, if we use the first three terms of the series, we get:
[tex]f(x) = x^2 + x^3 + x^4/2![/tex]
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